I’m going to be writing a story, and I want the math in it to be accurate, so I need some help with one part.
Imagine you’re traveling at the speed of light (299,792,458 m/s^2) and you start slowing down at a rate of 1G (9.81 m/s). How far will you have traveled after 1 day (86,400 seconds).
I’m not looking for the answer as much as I’m looking at how to solve for the answer because the length of time could change depending how I want things to proceed.
Thank you in advance.
In 86400 seconds you lose 86400 * 9.81 m/sec. On average, you lose half of that. So subtract that half from 299792458 m/sec, and multiply that average speed by 86400 seconds to get how far you go in those 86400 seconds.
If V is your initial velocity, and g is your deceleration, and t is the length of time, then the distance traveled is Vt - (1/2)gt^2, or (V - gt/2)*t
Pass your paper to the front of the row, and check your answer.
Your units are screwy. G is an acceleration, and it’s units are m/sec[sup]2[/sup].
you’re right. I meant to put s^2 for 1G, not for the speed of light.
I take it you’re completely ignoring relativity? From a relativistic point of view, your question is nonsense. If you chose g because you think that your characters would experience Earth gravity, you really don’t understand physics. A person going from c to c-adt in dt (where c= speed of light, a= acceleration and dt= differential time) would experience infinite acceleration.
No, I’m choosing G NOT because of gravitational pull, of which there is barely any in a spaceship, but because that rate of acceleration is comfortable to humans. Theoretically, one could accelerate from a standstill to the speed of light in about 353-354 days at a contstant acceleration of 1G and not feel uncomfortable during the trip. The same as when slowing down after hitting the speed of light.
As far as relativitics is speaking, I’m talking about time as far as the people within the spaceship are concerned. A week is still a week, and time does continue onward when you’re travelling at below the speed of light.
Now my guess as to the answer to my own problem is somewhere close to Sigma of 1 through N of (C-(9.81*N)
where C is the speed of light. Is this close?
Another question, which I might be needing but is purely hypothetical in nature. You’re traveling in a spaceship on a straight line at 99% the speed of light. You turn. What happens? Is there a point when the turn becomes too steep and you’re plastered against the wall in molecular form? Is any change in course a deathwish, or can you ride along with the curve with no adverse effects?
I’m afraid that your physics is quite a bit off, Enderw23.
It requires an infinite amount of energy to accelerate something with rest mass to the speed of light with respect to any rest frame. If such a thing existed, it would have infinite mass. The rest of the universe would immediately proceed toward it at the speed of light, and no more time would be experienced by anything in the universe, including the object in question.
There would be no way to slow it down.
One could not accelerate to the speed of light in any amount of time at 1G acceleration.
A few very basic bits about relativity: all motion is relative… that’s where the name comes from. There is no universal ‘stopped’ state. Whenever you state a velocity it is relative to some other object or reference frame. If you’re in a spaceship moving at .99c with respect to, say, the earth, to you it looks like the rest of the galaxy is moving rapidly in the other direction. You can accelerate in any direction you wish, it’ll all look like normal acceleration to you. The limits on acceleration in your reference frame will be the same as if you were in any other reference frame. To the observer on earth it’ll look like you’re accelerating much more slowly than you experience it, because earth will be experiencing time more rapidly than you will be. That’s why your 1G argument is flawed; if you’re experiencing time at 1/10 the rate of earth you must accelerate at 10G to make the observer on earth think you’re accelerating at 1G. As you approach c, your acceleration in your frame must become infinite to make the earth-bound observer see 1G acceleration, as the time you experience becomes slower with respect to that frame.
If you’re not that interested in relativity, perhaps you should just not delve into those details. It’s better to gloss over such things than to mention them and get them wrong…
If you want to read an SF book which uses relativistic velocities as part of the plot, I’d recommend Tau Zero by Poul Anderson.
Is it important to your story that the ship be going at exactly c, or would a nice, comfortable .9 c work just as well? If it has to be c, then you’re already invoking some physics counter to what is now known (heck, it is science fiction, after all), so you can just invoke that same physics to justify any answer you want for the deceleration time-- Just say that it takes 3.261 weeks for the warp coils to cool down, or whatever.
I fully expect to gloss over some bits of it.
Here’s the basic premise in three sentences. A supernova is seen some 2000 light years away. Scientists, wanting to further investigate this phenomenon, send people to this star BEFORE it goes supernova by traveling faster than light. Once there, they create a disruption which actually causes the supernova in the first place.
Bah, you say, there are so many problems with this premise. That’s why it’s science fiction, and not an article from the scientific journals. Of course you can’t travel faster than the speed of light, and, even if you could there’s no guarantee you’ll go backwards in time. It would take infinite fuel to get to C. One lone spaceship is going to cause a reaction for an entire star?
I’ve got solutions to most of these problems, and they’re not all “logical.” In science fiction, I have the luxury of creating solutions that aren’t exactly feasible. What I want to do, though, is try to stay as scientifically accurate as I can before I have to deviate off into my own premise.
I’m trying to determine the outcome as well. Can the people in the spaceshuttle escape inherent doom? Can they escape from slamming into the star without plastering themselves against the walls? The answers I get here will help shape this story.
Well, this seems reasonable. Your story involves FTL travel and time travel, which is fine; there are lots of excellent SF stories with those plot elements.
That being said, it’s more plausable to skip the near-c velocities entirely if you want faster-than-light (FTL) travel. Just call it warp speed, or wormholes, or hyperspace, or folding of space, etcetera. Alternatively, with time travel you could have them time travel 4001 years into the past and travel there at and average of .5 c. (FTL travel and time travel are physically analogous, but that’s another discussion.) As long as you’re going to go FTL anyway, why go to near-c velocities anyway?
Whatever explanation you use for FTL might determine whether they can escape with it or not. Is the FTL method easy to use, require time to set up, usable within a solar system, etc?
One plot possibility which would actually use near-c speeds would be that moving at near-c away from the supernova would red-shift the radiation to less energetic radiation, and slow the relative speed of the massive particles. Depending on your fictional radiation and particle shielding, this might make the difference for survival and be a plot point.
My acceleration is based upon panels which completely cover the ship that can convert all forms of electromagnetic waves it encounters into usable energy for propultion (it’s just crazy enough to work!).
I’ve decided that, for this story at least, it would take approximately 353 days on both sides of the FTL shift to reach their destination. Two years travelling inside this spaceship, one way. About 47 months round trip. The good news is that when they hit C, they can pretty much go anywhere in the universe instantly, so distance isn’t a problem, just time.
I’m continually developing branches to the story depending on how I want to take it. Ultimately, though, it should revolve around the basic premise that they created the very phenomenon that they went to investigate. Whether they live or die because of it is up for grabs. Morbid, I know.
Do they die? I’m not sure. They don’t have any “inertial dampeners,” or other such ST lingo to help them out. Because of sabotage, they come out of the FTL travel dangerously close to the star and need to turn to avoid it. But doing so could make them just as dead. They certainly can’t slam on the breaks. Seatbelts ain’t gonna help at that velocity. What happens? Stay tuned next week. Same bat time, same bat channel.